4 Practice Worksheet Assignment
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Week 4 Practice Worksheet Assignment
Week 4 Practice Worksheet Assignment
Prepare a written response to the following questions. Type your answers in the shaded boxes below. Each correct answer is worth one point unless otherwise noted. Week 4 Practice Worksheet is worth 7 points.
Chapters 9 &11
1. Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America’s Cup race. They race over a part of the course several times. The sample times in minutes for the Prada were: 12.9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3. The sample times in minutes for the Oracle were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and 19.0. For data analysis, the appropriate test is the t-Test: Two-Sample Assuming Unequal Variances.
The next table shows the results of this independent t-test. At the .05 significance level, can we conclude that there is a difference in their mean times? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means.
| Hypothesis Test: Independent Groups (t-test, unequal variance) | |||||||
| Prada | Oracle | ||||||
| 12.170 | 14.875 | mean | |||||
| 1.056 | 2.208 | std. dev. | |||||
| 10 | 12 | n | |||||
| 16 | df | ||||||
| -2.7050 | difference (Prada – Oracle) | ||||||
| 0.7196 | standard error of difference | ||||||
| 0 | hypothesized difference | ||||||
| -3.76 | t | ||||||
| .0017 | p-value (two-tailed) | ||||||
| -4.2304 | confidence interval 95.% lower | ||||||
| -1.1796 | confidence interval 95.% upper | ||||||
| 1.5254 | margin of error | ||||||
2. The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amount customers will purchase on impulse. A sample of ten customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85. A sample of fourteen customers at the Plum Street store revealed they spent the following amounts more than they planned when they entered the store: $18.19, $20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40, $20.57, $19.79, $14.83. For Data Analysis, a t-Test: Two-Sample Assuming Unequal Variances was used.
At the .01 significance level is there a difference in the mean amount purchased on an impulse at the two stores? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means.
| Hypothesis Test: Independent Groups (t-test, unequal variance) | ||||||
| Peach Street | Plum Street | |||||
| 15.8680 | 18.2921 | mean | ||||
| 2.3306 | 2.5527 | std. dev. | ||||
| 10 | 14 | n | ||||
| 20 | df | |||||
| -2.42414 | difference (Peach Street – Plum Street) | |||||
| 1.00431 | standard error of difference | |||||
| 0 | hypothesized difference | |||||
| -2.41 | t | |||||
| .0255 | p-value (two-tailed) | |||||
| -5.28173 | confidence interval 99.% lower | |||||
| 0.43345 | confidence interval 99.% upper | |||||
| 2.85759 | margin of error | |||||
3. Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?
| Hypothesis Test: Independent Groups (t-test, pooled variance) | |||||||
| Larry | George | ||||||
| 4.77 | 5.02 | mean | |||||
| 1.05 | 1.23 | std. dev. | |||||
| 40 | 50 | n | |||||
| 88 | df | ||||||
| -0.25000 | difference (Larry – George) | ||||||
| 1.33102 | pooled variance | ||||||
| 1.15370 | pooled std. dev. | ||||||
| 0.24474 | standard error of difference | ||||||
| 0 | hypothesized difference | ||||||
| -1.02 | t | ||||||
| .3098 | p-value (two-tailed) | ||||||
| -0.73636 | confidence interval 95.% lower | ||||||
| 0.23636 | confidence interval 95.% upper | ||||||
| 0.48636 | margin of error |
4. For each of the following studies, state whether a t test for dependent means or a t test for independent means is appropriate.
a. A researcher measures the heights of 40 unidersity students who are the firstborn in their families and compares the 15 who come from large famliies to the 25 who come from smaller families.
b. A researcher tests math skills of 250 individuals before and after they complete a one day seminar on managing test anxiety.
c. A researcher compares the resting heart rate of 15 individuals who have been taking a particular drug against the resting heart rate of 48 other individuals who have not been taking the drug.
Chapter 11
5. A physician who specializes in weight control recommends three different diets. As an experiment, 15 patients are randomly selected and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted. At the .05 significance level, is there a difference in the mean amount of weight loss among the three diets?
| Plan A | Plan B | Plan C |
| 5 | 6 | 7 |
| 7 | 7 | 8 |
| 4 | 7 | 9 |
| 5 | 5 | 8 |
| 4 | 6 | 9 |
An ANOVA was run and the results are shown below. At the .01 significance level, is there a difference in the weight loss between the three plans? What is the p-value? What can you do to determine exactly where the difference is?
| One factor ANOVA | ||||||
| Mean | n | Std. Dev | ||||
| 5.0 | 5 | 1.22 | Plan A | |||
| 6.2 | 5 | 0.84 | Plan B | |||
| 8.2 | 5 | 0.84 | Plan C | |||
| 6.5 | 15 | 1.64 | Total | |||
| ANOVA table | ||||||
| Source | SS | df | MS | F | p-value | |
| Treatment | 26.13 | 2 | 13.067 | 13.52 | .0008 | |
| Error | 11.60 | 12 | 0.967 | |||
| Total | 37.73 | 14 |
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